Dendriform Algebras Relative to a Semigroup
Loday's dendriform algebras and their siblings, pre-Lie and zinbiel, have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each operation is replaced by a family of operations indexed by a fixed se...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210782 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dendriform Algebras Relative to a Semigroup. Marcelo Aguiar. SIGMA 16 (2020), 066, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Loday's dendriform algebras and their siblings, pre-Lie and zinbiel, have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each operation is replaced by a family of operations indexed by a fixed semigroup . The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra, but in reference to the monoidal category of -graded vector spaces.
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| ISSN: | 1815-0659 |